Earth Syst. Sci. Data, 12, 137–150, 2020https://doi.org/10.5194/essd-12-137-2020© Author(s) 2020. This work is distributed underthe Creative Commons Attribution 4.0 License.

Global River Radar Altimetry Time Series (GRRATS):new river elevation earth science data records for the

hydrologic community

Stephen Coss1,2, Michael Durand1,2, Yuchan Yi1, Yuanyuan Jia1, Qi Guo1, Stephen Tuozzolo1,C. K. Shum1,6, George H. Allen3,4, Stéphane Calmant5, and Tamlin Pavelsky3

1School of Earth Sciences, The Ohio State University, Columbus, Ohio, USA2Byrd Polar and Climate Research Center, The Ohio State University, Columbus, Ohio, USA

3Department of Geological Sciences, The University of North Carolina at Chapel Hill,Chapel Hill, North Carolina, USA

4Department of Geography, Texas A&M University, College Station, TX, USA5IRD/LEGOS, 16 Avenue Edouard Belin, 31400 Toulouse, France

6Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China

Correspondence: Stephen Coss (coss.31@osu.edu)

Received: 23 May 2019 – Discussion started: 1 August 2019Revised: 9 November 2019 – Accepted: 26 November 2019 – Published: 22 January 2020

Abstract. The capabilities of radar altimetry to measure inland water bodies are well established, and severalriver altimetry datasets are available. Here we produced a globally distributed dataset, the Global River RadarAltimeter Time Series (GRRATS), using Envisat and Ocean Surface Topography Mission (OSTM)/Jason-2 radaraltimeter data spanning the time period 2002–2016. We developed a method that runs unsupervised, withoutrequiring parameterization at the measurement location, dubbed virtual station (VS) level, and applied it to allaltimeter crossings of ocean-draining rivers with widths > 900 m (> 34 % of the global drainage area). Weevaluated every VS, either quantitatively for VS locations where in situ gages are available or qualitatively usinga grade system. We processed nearly 1.5 million altimeter measurements from 1478 VSs. After quality control,the final product contained 810 403 measurements distributed over 932 VSs located on 39 rivers. Available in situdata allowed quantitative evaluation of 389 VSs on 12 rivers. The median standard deviation of river elevationerror is 0.93 m, Nash–Sutcliffe efficiency is 0.75, and correlation coefficient is 0.9. GRRATS is a consistent,well-documented dataset with a user-friendly data visualization portal, freely available for use by the globalscientific community. Data are available at https://doi.org/10.5067/PSGRA-SA2V1 (Coss et al., 2016).

1 Introduction

Despite growing demand from emerging large-scale hydro-logic science and applications, global and freely availableobservations of river water levels are still scarce (Hannah etal., 2011; Pavelsky et al., 2014; Shiklomanov et al., 2002).Advances in remote sensing and computing capabilities haveenabled new areas of global fluvial research that are de-pendent upon river elevations, including global hydrologicquantification of carbon and nitrogen fluxes (e.g., Allen andPavelsky, 2018; Oki and Yasuoka, 2008) and characteriza-

tion of flood risk for future climate scenarios (Schumannet al., 2018; Smith et al., 2015). Evaluation of these globalriver elevation models requires global datasets of river eleva-tion time series, but in situ river water levels are scarce, asthey are often not shared outside specific government agen-cies. Thus model evaluation and calibration increasingly re-lies on remotely sensed data (Overton, 2015; Pavelsky et al.,2014; Sampson et al., 2015). Newer radar altimeter missionslike Sentinel-3 are improving the contemporary record withfeatures like automated processing, alleviating the need forretracking and other postprocessing to generate useful mea-

Published by Copernicus Publications.

138 S. Coss et al.: Global River Radar Altimetry Time Series (GRRATS)

surements. In addition, the Surface Water and Ocean Topog-raphy (SWOT; https://swot.jpl.nasa.gov/, last access: 24 Oc-tober 2019) satellite mission, scheduled for launch in 2021,will observe global river elevations with an unprecedentedglobal spatial resolution despite variation within its mea-surement swath. Establishing robust global river elevationdatasets for the pre-SWOT period is critical to prepare for theSWOT mission and for the study of hydrology more broadly.

Satellite radar altimetry data have enabled important sci-entific advances in hydrology (Birkett et al., 2002; Bjerklieet al., 2005; Calmant et al., 2008; Jung et al., 2010; Getiranaet al., 2009; Birkinshaw et al., 2014; Frappart et al., 2015;Becker et al., 2018; Emery et al., 2018, among many others),but spatial coverage is limited. This is for two primary rea-sons: inclination or latitude coverage limits of radar altimeterorbits (orbits with better temporal resolution have worse spa-tial coverage), and technical measurement challenges associ-ated with retrieving elevation over seasonally varying rivers.Indeed, radar altimeter orbits and elevation retrieval technol-ogy were originally designed for characterizing ocean sur-face topography. The orbital characteristics of historic andcontemporary radar altimetry missions used for hydrologytend to follow either the 10 d TOPEX/POSIEDON, Jason-1,Jason-2, and Jason-3 orbit with relatively high temporal res-olution but low spatial coverage or the 35 d ERS-1, ERS-2,Envisat, and SARAL-AltiKa orbits with low temporal res-olution but higher spatial coverage. Neither of these orbitparadigms captures all global rivers (Alsdorf et al., 2007).

The second fundamental cause of poor global coverage ofriver radar altimeter observation availability is rooted in themeasurement itself. There are a set of criteria, such as riverwidth, nearby topography, and groundcover, associated withsuccessful water surface level retrieval, but none have beenshown to be fully predictive of water level accuracy (Maillardet al., 2015). Most of Earth’s rivers are too narrow to be accu-rately measured by satellite radar altimeters: Lettenmaier etal. (2015) suggest that rivers should be wider than 1000 m foroptimal retrieval, primarily due to the 1–2 km footprint sizeof pulse-limited satellite altimeters. Radar altimeter effectivefootprint size is a function of the surface characteristics andpulse emission mode. For example, in low-resolution mode(LRM), which was commonly used for satellite altimetersuntil ∼ 2016, footprints typically range from 1.5 to 6.0 kmin diameter, depending on the land topography near rivers.Thus, all but the widest rivers are (technically) subfootprintfeatures in LRM. Radar altimetry retrieval of river surface el-evations thus relies on the fact that rivers reflect more radarsignal than does land, due to the high dielectric constant ofwater. Some studies have developed methods to process radaraltimetry data for far narrower rivers with LRM altimeters(e.g., ∼ 100 m) for a particular location (e.g., Santo da Silva,2010; Maillard et al., 2015; Boergens et al., 2016; Bianca-maria et al., 2017). Since ∼ 2016, retrieving water levelsover narrow rivers is increasingly common with the syntheticaperture radar (SAR) altimetry missions (e.g., Cryosat-2 and

Sentinel-3) for which the equivalent footprint (300 m widealong flight track band) enables much easier detection andprocessing of radar returns from rivers.

Regardless of the specifics of a particular measurement lo-cation, altimeter range data (direct sensor measurement) re-quire a great deal of processing to be converted into usablesurface heights. Measurements of ocean height rely on anonboard processor known as a “tracker” to dynamically esti-mate the approximate range of the target (i.e., the sea surface)in order to map received radar pulses to precise surface eleva-tions. The onboard tracker works well for measuring oceansurface elevations, but it is unsuitable for estimating conti-nental surface elevations. It thus requires further processingsteps, known as “retracking”. Using retracked river observa-tions, inland radar altimetry can accurately measure chang-ing river surface elevation (Koblinsky et al., 1993; Berry etal., 2005; Frappart et al., 2006; Alsdorf et al., 2007; Santosda Silva et al., 2010; Papa et al., 2010; Dubey et al., 2015;Tourian et al., 2016; Verron et al., 2018). While custom re-trackers have been derived and tested in particular locations(Huang et al., 2018; Maillard et al., 2015; Sulistioadi et al.,2015) the ICE-1 retracker (Wingham et al., 1986) is arguablythe best compromise between being consistently reliable andavailable for many altimeter missions (Biancamaria et al.,2017; Frappart et al., 2006; Santos da Silva et al., 2010).While available globally, the ICE-1 retracked data must beextracted over river targets, and carefully filtered, to makethem useful to global hydrological modeling applications.

The four currently available radar altimeter datasetsfor rivers represent tremendous technical achievements:(1) Hydroweb (http://hydroweb.theia-land.fr/, last access: 3January 2019), (2) Database for Hydrological Time Seriesover Inland Waters (DAHITI) (https://dahiti.dgfi.tum.de/en/,last access: 3 January 2019), (3) River&Lake Near Real Time(NRT) (https://web.archive.org/web/20181006062149/http://tethys.eaprs.cse.dmu.ac.uk/RiverLake/shared/main, last ac-cess: 3 January 2019), and (4) HydroSat (http://hydrosat.gis.uni-stuttgart.de/php/index.php, last access: 3 January 2019).However, they are not optimized for the specific needs ofglobal hydrologic modelers, who require global coverage andenhanced ease of use (accessibility and metadata). Note thatRiver&LakeNRT is no longer online but we compare againstit for historical reasons (an archive link has been provided).Existing datasets have several characteristics that make themchallenging to use for global hydrologic modeling. First, theytend to include dense coverage where altimeters perform well(e.g., over large, tropical rivers) or are based on program-matic priorities of funding agencies. Hydroweb has 991 riverVSs in South America alone, for example, primarily in theAmazon basin, while most include few Arctic rivers. Onechallenge of including Arctic rivers involves the complicat-ing effect of river ice, which is widespread for much of theyear. Three of the four datasets (Hydroweb being the ex-ception) cannot be downloaded in bulk but require repetitiveclicking via web interface.

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S. Coss et al.: Global River Radar Altimetry Time Series (GRRATS) 139

In this study, we determined what fraction of availablealtimeter data would be useful for global rivers using re-tracked data available from the official distribution of theinstrument data (the geophysical data records, GDRs), un-supervised methods, and automatic data filtering processes.The result is the Global River Radar Altimetry Time Series(GRRATS), a global river altimetry dataset comprised of anopportunistic exploitation of VSs on the world’s largest riversspecifically suited for the needs of global hydrological ap-plications. GRRATS uses the VS as its fundamental organi-zational element. VSs are locations where ground tracks ofexact repeat altimetry mission orbits cross rivers, enablingthe development of a time series of water elevation observa-tions. VSs can be thought of much in the same way as anin situ river gaging station but are entirely derived from re-motely sensed measurements of river surface elevation. GR-RATS is an Earth Science Data Record (ESDR) hosted atthe Physical Oceanography Distributed Active Archive Cen-ter (PO.DAAC) with a focus on conforming to data manage-ment and stewardship best practices (Wilkinson et al., 2016).GRRATS currently spans 2002–2016 and includes globalocean-draining rivers greater than 900 m in width: these col-lectively drain a total of > 34 % of global land area. GR-RATS follows data management best practices as outlined byWilkinson et al. (2016), and it includes extensive metadata.In developing GRRATS, our purpose is to create an accuratedataset, and also to create a better data product focused onease of use.

2 Methods

There are four major steps in building GRRATS (Coss etal., 2016): (1) identification of potential VSs on globalrivers, (2) extraction of altimeter observations from the geo-physical data records (GDRs), (3) filtering out noisy re-turns from the altimetry, and (4) performing either quantita-tive of qualitative evaluation. The philosophy and overviewof GRRATS methods are reviewed here, whereas detailsof GRRATS production are more thoroughly describedin the user handbook (ftp://podaac-ftp.jpl.nasa.gov/allData/preswot_hydrology/L2/rivers/docs/, last access: 3 January2019).

2.1 Identification of potential VSs

We began by identifying potential VSs for GDR extrac-tion by identifying locations on global ocean-draining riverswhere altimeter orbital ground tracks cross river locationsgreater than 900 m in width. We chose 900 m as our lowerwidth limit as previous work has shown that VSs with widths> 1 km present a higher probability of good performance(Birkett et al., 2002; Frappart et al., 2006; Kuo and Kao,2011; Papa et al., 2012). This selection of rivers is spatiallyvaried and large enough to provide a sensible constraint onglobal models. We used the intersection of the nominal al-

timeter ground tracks with the Global River Widths fromLandsat (GRWL) dataset to identify such locations (Allenand Pavelsky, 2018).

2.2 GDR extraction

We extracted altimeter observations at the VS from theGDRs; this consisted of three steps. First we spatially joinedLandsat imagery (selected from times of mean river dis-charge) compiled for the Global River Widths from Land-sat (GRWL) river centerlines dataset (Allen and Pavelsky,2015, 2018) with satellite ground tracks to define the widthextent of the mask used for the extraction of water eleva-tions. Each mask was constructed using the width extent andupstream and downstream limits that were 2 km perpendicu-lar to the crossing location. We extracted all altimeter returnswith centroids falling within each mask for each pass fromJason-2 GDR version D (Dumont et al., 2009) and the En-visat GDR, version 2.1 or later (Soussi and Féménias, 2009),using corrections outlined in product documentation. We ex-tracted ICE-1 retracked ranges from the GDR (Gommengin-ger et al., 2011; Wingham et al., 1986). To get ellipsoidalheights, we applied the standard combination of parametersand corrections. We then converted these ellipsoidal heightsto an orthometric height above the geoid, using the EarthGravitational Model 2008 (EGM08; Pavlis et al., 2012).

2.3 Data filtering

We filtered altimetry data in a six-step process. First, we fil-tered using an a priori digital elevation model (DEM) databaseline elevation (median of all best available DEM valuesfalling within the extraction polygon) at each VS. We usedShuttle Radar Topography Mission (SRTM), Global Multi-Resolution Terrain Elevation Data (GMTED), and AdvancedSpaceborne Thermal Emission and Reflection Radiometer(ASTER), in that order of preference (Abrams, 2000; Daniel-son and Gesch, 2011; Van Zyl, 2001). We filtered out el-evations 15 m above or 10 m below the constrained base-line elevation. We arrived at these limits by examining over150 United States Geological Survey (USGS) gages with up-stream drainage areas larger than 20 000 km2 and changingthe upper filter limit (responsible for 90.5 % of data pointsfiltered due to height) to 14 or 16 m, resulting in a 4.2 %increase and 3.8 % decrease in filtered points respectively.We determined these limits should reasonably encompassany measurements of the river surface as the Amazon floodwave is capped around 15 m from trough to peak (Trigg etal., 2009). Second, we applied an additional elevation filterremoving any elevations that fell 2 m or more below the 5thpercentile of surface elevations in the time series (0.03 % oftotal returns). We obtained low-end filter criteria for remov-ing observations impacted by near-river topography at lowflow by trial and error. Third, we flagged and removed eleva-tions from times of likely ice cover. Ice cover dates were de-

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termined from USGS and Environment and Climate ChangeCanada (ECCC) data when available. If ice breakup datawere not available, we applied broad date limits regionally,using observations from the Pavelsky and Smith (2004) studyof Arctic river ice breakup timing. Breakup dates range fromlate September to early June. Fourth, remaining elevationswere averaged for each cycle at each VS. Fifth, we removedany potential VS with < 25 % or 50 % of available cycles forrivers with and without ice cover, respectively. Finally, wedetermined a flow distance limit for tidal VSs (those wherethe tidal signal was dominant) using visual inspection of thetime series on each river and removed VSs below that point.

2.4 Data evaluation

We acquired evaluation stage data from 65 stream gages (on12 rivers) (Environment Canada, 2016; Jacobs, 2002; Mar-tinez, 2003; USGS, 2016). All stage data are publicly avail-able with the exception of data from the Congo, Ganges,Brahmaputra, and Zambezi, which were provided by the au-thors. Note that VSs rarely fall in the same location as astream gage; thus, most studies recommend some VS–in situstream gage distance (e.g., 200 km) beyond which compar-isons are not performed (Michailovsky et al., 2012). Anal-yses showed that VS–stream gage distance was often notan accurate predictor of height anomaly differences. Thisis likely due to the hydraulics (width, nearby dams, conflu-ences) of a more distant gage being more similar to the lo-cation of the VS than the most proximal gage. Thus, in thisstudy, we compared each virtual station with all in situ gagesavailable on the main channel of that river. At each VS, wereported error metrics for the best, median, and the spatiallyclosest comparison. For completeness, we included VSs withpoor error metrics; users can then select which of the VSsto use, based on their reported error statistics and the userapplications. Following the normal practice in the field (e.g.,Berry and Benveniste, 2010; Schwatke et al., 2015), we com-pare relative heights between VSs and gages, as opposed toabsolute heights, in order to avoid the influence of the differ-ence in datum and the lack of correspondence between satel-lite ground tracks and gage locations. We calculated relativeheights by removing the long-term mean between the sam-ple pairs of VS heights and the stage measured by the streamgages. Error metrics in GRRATS include the correlation co-efficient (R), Nash–Sutcliffe efficiency (NSE), and standarddeviation of the errors (SDEs). NSE is typically employed todescribe the goodness of fit for a modeled result with mea-sured values, so our use here is nontraditional. Nonetheless,we use NSE because, as opposed to R and SDE, NSE nor-malizes error with variation from the mean in the observed,or in our case, in situ data, by comparing error to actual vari-ability. For example, 1 m of error can be an issue of varyingseverity when rivers can have height variation ranging from> 10 m (Amazon) to < 5 m (Saint Lawrence River). It is also

an established metric for goodness of fit within the altimeterliterature (Biancamaria et al., 2018; Tourian et al., 2016).

While qualitative grades are not as reproducible as bestfit statistics, they have been used in the past to guide usersto preferable time series when no other error metrics areavailable (Birkett et al., 2002). For the remainder of our VSs(without stage gages), we performed a qualitative evaluationof the station represented by a letter grade ranging from A(highest level of confidence on the data quality) to D (lowestlevel of confidence). The criteria used in the assignment ofletter grades were based on the presence of obvious outliers,number of data points in the time series, and time series con-tinuity with nearby VSs. We determined outliers by visualinspection. Letter grades take into consideration all of thesecriteria, but in general VSs with an A rating would have oneor fewer obvious outliers per year, would have no more thantwo cycles filtered out per year, and would fit nicely aboveVS downriver and below VS upriver. A D rating might beapplied to a VS with three or more outliers per year and withfive or more cycles missing per year, and it might fall belowVS downriver from it and above VS upriver from it. We ex-plicitly recorded and document which VSs in GRRATS areevaluated using this qualitative approach.

3 Results and discussion

GRRATS processing produced a total of 932 globally dis-tributed virtual stations (Fig. 1). The 39 GRRATS rivers ac-count for 50 million km2 (> 34 %) of the global drainage areaand include 13 Arctic rivers. To attain these results, we ex-tracted and processed a total of 1.5 million individual radarreturns at 1478 potential VS locations.

3.1 Filtering returns

We removed 309 700 altimetry returns with our height filters(steps 1 and 2 of our filtering process), leaving 1.1 million(78.2 %) viable measurements. Our ice filter removed an ad-ditional 296 900 of the remaining returns (step 3) resulting in810 400 viable returns (57.2 %). Averaging all height returnswithin the river polygons for each pass at each VS (step 4) ledto a total of 102 300 (21 900 on Arctic rivers) pass-averagedmeasurements. VSs were required to retain 50 % (withoutice) or 25 % (with ice) of their passes postfiltering to be in-cluded in the final data product, resulting in the removal of465 potential VS locations (step 5). VSs were also removedby visual inspection if they were tidal, resulting in the re-moval of an additional 45 stations (step 6). While many VSswere filtered heavily, 72.8 % of the total returns for all VSs inthe final product passed all filters (the median VS value be-ing 97.7 %) and 227 VSs lost no returns. The filtering processresulted in a total 932 VSs for evaluation derived from stan-dard retracked data (ICE 1). These VSs had a dataset-wideaverage of ∼ 16 measurements per year (9.5 for Envisat VSsand 35.8 for Jason2 VSs).

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Figure 1. The GRRATS dataset and evaluation results. Maximum NSE (best fit) plotted in yellow to red (shown on all rivers with gage data)and qualitative grades plotted in teal to dark purple. In both cases, darker colors indicate better evaluation results. Each river is evaluatedusing only one of these methods.

3.2 Example time series evaluation

Figure 2 shows example GRRATS time series for theMackenzie and Amazon Rivers and corresponding in situgages. Error bars represent the range of the values that wereaveraged to generate each data point (does not include fil-tered data points). Data necessary to compute error bars area part of the data product. Comparison between the Jason-2 time series and the gage on the Mackenzie River pro-duced SDE= 0.5 m, NSE= 0.41, and R = 0.64. In this case,the gage used for evaluation was located ∼ 700 km upriver(Fig. 2a). The SDE is approximately consistent with what isexpected from the literature (Asadzadeh Jarihani et al., 2013;Frappart et al., 2006). However, the SDE is relatively large incomparison with the overall annual range in the time series(typically ∼ 2 m) observed from the gage (see Fig. 2a), lead-ing to a relatively low NSE. Additionally, several cycles havefar larger errors, reaching up to 2 m in some cases. Thereare a total of three in situ gages used for evaluation on theMackenzie River. Across the three gage comparisons, thisVS had median statistics of 0.58 m, 0.35, and 0.64 for SDE,NSE, and R, respectively. Comparing the VS data to the gageon the Amazon River yields SDE= 0.98 m, NSE= 0.94 andR = 0.97, with the evaluation gage 263 km upriver from theVS (Fig. 2b). Despite the SDE being nearly twice as large,the magnitude of change on the Amazon allowed for a muchbetter fit due to the large interannual variability of the Ama-zon flood wave (> 10 m). Most of the error was from timesof low flow near the ends of the calendar year in 2009, 2011,and 2012. There are six in situ gages on the Amazon River.Across these comparisons, this VS had median statistics of0.94 m, 0.95, and 0.98 for SDE, NSE, and R, respectively.

Table 1. Summary statistics from Sect. 3.3.

Fitstatistic Best Closest Median

NSE Highest Median Median Highest Median0.98 0.75 0.67 0.96 0.31

R Highest Median Median Highest Median0.99 0.9 0.87 0.99 0.69

SDE Lowest Median Median Lowest Median0.11 m 0.93 m 1.08 m 0.31 m 1.3 m

3.3 GRRATS evaluation across all rivers

We compared GRRATS against in situ evaluation data ona total of 12 rivers. This provided evaluation of 380 of the920 virtual stations (42 %). On each river, the total numberof time series evaluations was the product of the number ofVSs and the number of gages (Fig. 1). Thus, the total numberof time series evaluations (summed across all 12 rivers) was1915 (Table 1).

A total of 72.5 % of the quantitatively evaluated virtualstations had an NSE greater than 0.4 when compared withat least one gage. The highest maximum NSE (Fig. 3a) was0.98, from an Envisat VS in the upper reaches of the Amazon.The median value for maximum NSEs for all VSs was 0.75(0.67 from closet gage comparison Fig. 3c). A total of 341of the 389 (87.7 %) virtual stations had a maximum NSE > 0(Fig. 3a) .The highest median NSE (Fig. 3b and values were0.96 at two Envisat VSs on the Orinoco river (lower and mid-dle). A total of 277 of 389 (71.2 %) had a median NSE > 0.

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Figure 2. Example time series for the Mackenzie River. Panel (a) shows water surface heights with ice filtering compared to the EnvironmentCanada gage (10KA001) located 684 km away from the virtual station. Panel (b) compares the time series derived from Jason-2 for one ofthe Amazon gages. Error bars represent the range of the values that were averaged to generate each data point (does not include filtered datapoints).

Figure 3. Virtual station fit statistics computed with all availableevaluation gages located in the same river and closest comparison.Please note that NSE values are plotted here only when greater than0 to enable readers to more easily see the majority of the data. A to-tal of 12.2, 28.8, and 17.2 % of the total data are not shown in panel(a), (b), and (c) respectively. (a) Histogram of the max NSE > 0at each VS in the dataset, (b) histogram of the median NSE > 0at each VS in the dataset, (c) histogram of the closest NSE > 0,(d) histogram of the minimum SDE in the dataset, (e) histogram ofthe median SDE of all the VSs in the dataset, (f) histogram of theclosest SDE, (g) histogram of the max R at each VS in the dataset,(h) histogram of the median R at each VS in the dataset, and (i) his-togram of closest R.

The smallest minimum SDE (to two significant digits) was0.11 m and occurred at an Envisat VS on the upper Congo.The median value for minimum SDE (Fig. 3d) for all VSswas 0.93 m (1.08 m from closest gage comparison Fig. 3f).The minimum and median values for median SDE (Fig. 3e)were 0.31 m and 1.3 m respectively. Our SDE error statisticsare greater than previous work reporting accuracies rangingfrom 0.14 to 0.43 m for Envisat data and 0.19 to 0.31 m forJason-2 data (Frappart et al., 2006; Kuo and Kao, 2011; Papaet al., 2012; Santos da Silva et al., 2010). This discrepancy islikely because GRRATS includes VSs on rivers where evalu-ations have not previously been reported in the literature andbecause of the fact that we do not fine-tune processing orfiltering to each VS due to the global nature of the dataset.

Some locations with relatively low SDE values showedpoor performance in terms of NSE, particularly for riverswith relatively low water elevation variability. VSs on theSaint Lawrence River had a minimum SDE ranging from0.58 to 3.27 m. The VS with a 0.58 m SDE correspondedwith a maximum NSE value of −0.27, indicating quite poorperformance in resolving river variations (standard deviationof 0.35 m). The Saint Lawrence River is anomalous in otherways as well. For two potential VSs (one each from Jason-2 and Envisat), the unprocessed data (ICE-1 retracked GDRdata) showed a bias of several tens of meters above the base-line height, and thus no data for these VSs are included inGRRATS. Closer examination of these VSs seems to indi-cate that the onboard tracking window was often tens of me-ters outside of the river surface range, making retrievals fromthe surface impossible. This case is particularly odd as sucherrors are not expected for wider rivers; the Saint LawrenceRiver is between 2 and 7 km wide where we sampled it. Sucherrors are more commonly associated with altimeter returns

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Table 2. Qualitative letter grade summary.

Grade A B C D

Number of VS 85 155 177 114with grade

from near-river topography on narrow rivers (Biancamaria etal., 2017; Frappart et al., 2006; Maillard et al., 2015; Santosda Silva et al., 2010). Moderately poor performance from theremainder of VSs in terms of NSE and SDE on the river islikely due to the river lacking enough variation in height toallow for retrieval of a good signal outside the error range ofradar altimeters. However, these low-variation data can stillbe quite useful to modelers for determining if their resultsshow excessive change in the annual cycle of water eleva-tions.

The median of the maximum R values (Fig. 3g) for eachstation is 0.9 (0.87 from closest gage comparison Fig. 3i).The maximum R value plot shows left skewness, similar tothe NSE results. The lowest maximum R value of −0.15 oc-curred at an Envisat VS on the middle Saint Lawrence River,which was the only virtual station to display a negative cor-relation. The best maximum R value was 0.99 for an En-visat station near the mouth of the Ganges River that alsodisplayed high NSE and low SDE. The median value of themedian R (Fig. 3h) is 0.69. The values range from−0.18 (anEnvisat VS on the lower Saint Lawrence River) to 0.99 (anEnvisat VS on the lower Brahmaputra).

For 27 of the 39 rivers in the GRRATS dataset, no in situdata are available for evaluation. We gave the remaining 27rivers qualitative letter grades based on number of missingdata points, obvious outliers, and agreement with nearby sta-tions. These grades are included with the data for end users(Table 2). The majority of rivers evaluated this way fall intothe B or C category (∼ 61 %), with only∼ 15 % getting an Arating.

3.4 Towards quantitative performance prediction

As is evident above, radar altimeter performance varies dra-matically across rivers and across VSs. Generally, measure-ments from wide rivers without large topographic features inthe altimeter footprints that have large seasonal water eleva-tion variations tend to result in better altimeter performance.In order to identify conditions that may contribute to poorreturn quality, we compared both VS width and percentageof original returns postfiltering, near-river topography, andriver height variation with all three fit statistics. We found nostatistically significant relationships in this evaluation, a find-ing that supports existing literature on quantitative predictionof altimeter performance (Maillard et al., 2015). Indeed, wefound many examples of counterintuitive performance in ourexamination. The Saint Lawrence River (described above) is

an example of unexpectedly poor performance; typical pre-dictors such as width (smallest VS ∼ 1.5 km wide) and thelack of extreme proximal topography led to an expectationof accurate performance that was not met. Meanwhile, otherrivers defied the normal pattern by showing good fit metricswhile being far narrower. The Mississippi River was con-sistently at our lower limit for river width. The VS widthsranged from 509.1 to 2 608.0 m and had an average width ofjust 955.3 m. The average near-river relief ranged from 10to 60 m. The Mississippi maximum NSE values ranged from−0.22 to 0.96, with an average of 0.43. Minimum SDE val-ues ranged from 0.34 to 2.22 m, with an average of 1.18 m.Additionally, we computed average error statistics across allVSs along each river. Some rivers stood out as particularlygood or poor performers (Table 3), but no broad geographicalpatterns emerged. For this reason, we recommend using themedian (dataset wide) value for the evaluated SDE (0.93 m)as an error estimate for VSs without evaluation data, as thisis representative of 42 % of all of the VSs in the dataset.While we do not provide error estimates at the individual datapoint level, we suggest that individual VS data point errors betreated as the SDE of the time series they are a component of.

3.5 Comparison to other altimetry datasets

While it is outside the scope of this study to compare GR-RATS exhaustively with existing datasets, we find it appro-priate to demonstrate that our dataset is comparable. There-fore, we compared three VS locations that are in each ofthe four datasets discussed (one on the Amazon, Congo, andBrahmaputra). Figure 4a–c show time series anomaly at eachVS and the closest gage. Note that time series lengths arelimited to the shortest time series in the comparison and donot match the coverage of any particular mission. Also notethat River&LakeNRT data were unavailable for the VS lo-cation shown on the Brahmaputra. GRRATS, DAHITI, andHydroweb are similar and fit with the in situ gage well (Ta-ble 4). DAHITI is missing data on the Amazon time series.HydroSat and River&LakeNRT are frequently out of phase,particularly on the Amazon River (Fig. 4a). Performance issimilar on ungaged rivers when compared (Fig. 5). GRRATSand DAHITI showed good agreement on the Paraná River(Fig. 5a). HydroSat and Hydroweb (Fig. 5b–c) are differ-entiated from GRRATS on the Ob and Lena rivers, as theyshow heights from a frozen river that GRRATS flags and re-moves. During overlap, HydroSat and GRRATS were similarat the Ob River VS. Hydroweb data on the Lena is similar toGRRATS, with the exception of the 2006 peak flow, whichis missing. Note that much of the rising limb is missing inthese time series as it occurs during times of ice cover. Unfil-tered data and ice flags are available to data users if needed.This process demonstrated that our quasi-automated methodsproduce a dataset with global coverage and performance thatapproximates the accuracy of regional altimetry datasets.

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144 S. Coss et al.: Global River Radar Altimetry Time Series (GRRATS)

Table 3. River average fit statistics.

Best average statistics Worst average statistics

Fit statistic River Value River Value

Maximum NSE BrahmaputraOrinocoAmazonGangesCongo

0.820.780.690.650.6

St. LawrenceSusquehannaColumbiaMackenzie

Max NSE < 0

Maximum R OrinocoBrahmaputraGangesCongo

0.930.920.870.85

St. LawrenceMackenzieColumbiaSusquehanna

0.30.460.490.68

Minimum SDE CongoYukonBrahmaputraMississippi

0.53 m0.76 m1.07 m1.18 m

MekongOrinocoMackenzieSt. Lawrence

2.61 m1.95 m1.88 m1.69 m

Figure 4. Multiproduct evaluation at the same location. Panel (a): multiproduct comparison on the Amazon River. Panel (b): multiproductcomparison on the Congo River. Panel (c): multiproduct comparison on the Brahmaputra river. DAHITI is plotted in purple with squaremarkers, HydroSat in dark blue with circle markers, River&LakeNRT (GNRTRL) in yellow with diamond markers, Hydroweb in red withcross markers, and GRRATS in green with x markers and in situ in dashed light blue. Note that the legend in panel (b) applies to all of Fig. 4.GRRATS error bars not shown to improve readability.

4 Data availability

GRRATS (https://doi.org/10.5067/PSGRA-SA2V1) for non-commercial use only (Coss et al., 2016). Data are providedin NetCDF format. For a file content description please seeAppendix A. An interactive map of the data is located athttp://research.bpcrc.osu.edu/grrats/ (last access: 6 Novem-ber 2018; Gou, 2017). This tool is intended for explorationonly and may not reflect the most-up-to-date version of thedata. As with Fig. 2, error bars represent the range of the val-ues that were averaged to generate each data point (does not

include filtered data points). Data necessary to compute errorbars are a part of the data product.

5 Conclusions

We find that uniform altimeter data processing produces us-able data with accessible documentation for end users. En-couraging end user understanding of how these kinds of dataare produced is critical in fostering its use across the scien-tific and stakeholder communities. GRRATS considers onlyocean-draining (highest order) rivers, while other datasets in-

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S. Coss et al.: Global River Radar Altimetry Time Series (GRRATS) 145

Figure 5. Multiproduct evaluation at ungaged river locations. GRRATS is plotted in green, DAHITI in purple with square markers, HydroSatin blue with circle markers, Hydroweb in red with cross markers, and times of ice cover with a dotted black line. Panel (a) is a comparisonwith DAHITI on the Paraná River. Panel (b) is a comparison with HydroSat on the Ob River. Panel (c) is a comparison with Hydroweb onthe Lena river.

Table 4. Multiproduct fit statistics from Fig. 5.

Product SDE R NSE

Amazon River

HydroSat 2.12 m 0.61 0.33Hydroweb 1.42 m 0.96 0.72GNRTRL 2.9 m 0.3 −0.74DAHITI 0.85 m 0.99 0.81GRRATS 1.57 m 0.95 0.65

Congo River

HydroSat 0.48 m 0.87 0.76Hydroweb 0.42 m 0.92 0.84GNRTRL 3.2 m 0.11 −7.88DAHITI 0.39 m 0.93 0.86GRRATS 0.5 m 0.91 0.81

Brahmaputra river

HydroSat 0.56 m 0.96 0.92Hydroweb 0.58 m 0.91 0.96DAHITI 0.6 m 0.96 0.86GRRATS 0.69 m 0.95 0.87

clude some VSs on large tributaries. However, our use of theGRWL dataset allowed for a comprehensive selection of al-timeter crossings on a global scale. These features should en-able broad use by the scientific community. This resulted inGRRATS having the best coverage available for North Amer-ican rivers as well. We produced GRRATS with ease of usein mind. VS metadata are included and the product can bedownloaded in bulk.

On the whole, the median value of the error standard de-viation is 0.93 m, which is similar to or slightly larger thanvalues reported for the rivers that are most commonly studiedusing radar altimetry (e.g., the Amazon and Congo). Our phi-losophy in constructing the dataset was to maximize the spa-tial coverage of altimeter crossings, to construct the productin a uniform way, and to provide an evaluation of quality foreach VS. Thus, users can decide whether each VS is usefulgiven their data needs. Note that a total of 77.2 % of virtualstations evaluated against in situ data had an NSE > 0.4. Ouruniform production method allowed us to evaluate whetherriver width or the height of bluffs proximal to rivers at altime-ter crossings correlates with altimeter performance, as wasexpected in the literature. However, we were unable to iden-tify a predictive model for altimeter performance and leavethis exercise for future work.

The GRRATS dataset maximizes traceability: all of the in-formation needed to reprocess these VSs is included in thefinal data product. It is our expectation that other researcherscould implement other methods of filtering and processing toachieve derived data products tailored to their applications.

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146 S. Coss et al.: Global River Radar Altimetry Time Series (GRRATS)

Appendix A: Data packaging and variableidentification

Table A1. The global variables are longitude and latitude of the center of the virtual station, the virtual station ID, the satellite name, flowdistance, sampling rate, the satellite pass number and a suite of fit statistics, or a qualitative letter grade. Qualitative letter grades were assignedbased on amount of data points, seasonal pattern, and similarity to nearby VS. This was done only when validation data were unavailable.When validation was possible, the VS was evaluated with all gages on the river through relative height comparison. Maximum Nash–Sutcliffeefficiency (NSE), average NSE, maximum R (correlation coefficient), minimum standard deviation of error (SDE), and average SDEs arereported.

Sample altimetry data (NetCDF format)Format: netcdf4 Title: Altimetry Data for virtual station Yukon_Jason2_0’Global variables

Variable Dimension Data type Units Name

long X double degrees east longitudelat Y double degrees north latitudeID root char – reference VS IDsat root char – satelliteFlow_Dist distance double km distance from river mouthrate root double Hz sampling ratepass root int32 – pass numberNSE grade double – max Nash Sutcliffe efficiencyNSE AVG grade double – average Nash–Sutcliffe efficiencyR grade double – correlation coefficientSD grade double m minimum standard deviation of errorSD AVG grade double m average standard deviation of errorgrade grade char – qualitative letter grade

Table A2. This includes the data from each return: long and lat, the height of the water level in meters, the signal strength, sigma0, indecibels, a “peakiness” value, the cycle number, the time of the return, and filter flags that signal 1 for data that should be included and 0 fordata that should be excluded. The flags are for a height filter, an ice filter, and the logical intersection of the two (allfilter), with 1 denotingreturns that pass through the filter and 0 denoting returns that do not.

Groups:unprocessed GDR data

Variable Dimension Data type Units Name

long X double degrees east longitudelat Y double degrees north latitudeh Z double meters above EGM2008 geoid unprocessed heightssig0 UGDR double dB sigma0pk UGDR double unknown peakinesscycle UGDR int32 unknown altimeter cycletime T double days since 1 Jan 1900 00:00:00heightfilter UGDR int32 -flag- good heights flagicefilter UGDR int32 -flag- no ice flagallfilter UGDR int32 -flag- ice-free heights that passed height filter

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Table A3. These are pass-averaged values, having gone through the filter. There are two values that flag data:−9999 for data that are missingfrom the GDR and −9998 for data that are missing because of height/ice filters. These flags are only present when none of the values to beaveraged can be found. The other values give average height (hbar), in meters, and sigma0 weighted height using.

Time series

Variable Dimension Data type Units Name

time T double days since 1 Jan 1900 00:00:00 timecycle TS int32 – altimeter cyclehbar Z double meters above EGM2008 geoid average heighthwbar Z double meters above EGM2008 geoid weighted average heightsig0bar time double dB average sigma0pkbar time double – average peakiness

Table A4. These are the data from the polygons, including the Landsat scene ID used to draw the polygons. The island flag is used whenislands are visible inside the polygon in the imagery when drawing the mask.

Sampling

Variable Dimension Data type Units Name

scene scene char – Landsat Scene IDlongbox X double degrees east longitude box extentlatbox Y double degrees north latitude box extentisland scene int32 -flag- island flag

Table A5. These are the filter data; nNODATA gives the number of cycles that have no data because of a lack of data in the GDR and/ordata that are filtered out. riverh gives the river elevation extracted from a 30 arcsec DEM of the region. This is used for the height filter. maxhand minh are the upper and lower bounds of river heights included in the filtered data; we set an elevation of +15 m or −10 m from theDEM river elevation as a first pass, and we then removed any data that was 5 m below the 5th percentile of river stage heights. icethaw andicefreeze are the thaw and freeze dates, respectively, for the years included in the altimetry dataset. The DEM used refers to the DEM thatthe baseline height was taken from.

Filter

Variable Dimension Data type Units Name

nNODATA – int32 count number of cycles without datariverh Z double meters above EGM2008 geoid river elevation from filter filemaxh Z double meters above EGM2008 geoid max elevation allowed by filterminh Z double meters above EGM2008 geoid min elevation allowed by filtericethaw T double days since 1 Jan 1900 00:00:00 thaw dates for rivericefreeze T double days since 1 Jan 1900 00:00:00 freeze dates for riverDEMused DEM char – DEM used in height filter

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Author contributions. SCo developed and finalized processingalgorithms, performed the methods exploration, was the pri-mary data manager, analyzed the final product, and finalized themanuscript. MD developed algorithms, performed the quality anal-ysis, and provided editorial and graphical assistance. YY performedthe GDR extraction and geodetic corrections and was the primaryunprocessed data manager. YJ performed the methods exploration.QG performed the methods exploration. ST developed algorithmsand performed the methods exploration. CKS provided technicalexpertise and editorial assistance. GHA and TP provided access tothe GRWL width data used to find the virtual station targets. SCaprovided technical expertise, in situ data, and editorial assistance.

Competing interests. The authors declare that they have no con-flict of interest.

Acknowledgements. We would like to acknowledge the use ofstream gage data and imagery obtained from the (i) USGS streamgage network and other organizations and (ii) USGS Landsatarchive, respectively, as well as altimeter VS data products fromother research institutes.

Financial support. This research has been supported by NASA(grant nos. NNX15AH05A and NNX13AK45A).

Review statement. This paper was edited by Ge Peng and re-viewed by two anonymous referees.

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